Fundamentally, CabSpotting’s data, cab-spots, are points
in space and time. Different views of cab activity come into focus by
looking at cab-spots at various scales of space and time.

Many CabSpotting images connect the dots for each cab to indicate its
path. Rendering the connected cab-spots for hundreds of cabs over the
span of about a month yields an image like this:

The numerous impossible strings crossing the bay indicate how often
there are long time-gaps between samples (see cabspotting_always_in_progress).
This temporal coarseness may be happening everywhere, but the bay’s
backdrop of inactivity reveals it best.

Details are completely lost in the pile of paths where activity is
greatest. Still, some main arteries emerge. But the spilt-ink density
in this image begs for fewer lines, or none.

Constellations

Looking only at spots gives star-gazing views of the data where you
see more details and patterns the longer you look. Beginning with a
very short span of time, the image below shows ten minutes of activity
across the middle of San Francisco, beginning at midnight on March 21st,
2007.

No obvious cityscape features pop out. Yet there are enough spots
to invite our eyes to connect dots and imagine a few streets, reminiscent
of picturing lively constellations from a handful of stars.

The next image shows the same space over 100 minutes, the original
10 and the hour and a half following them.

Streets begin to appear. The slant of Market Street is clearly visible
as it injects traffic into the city at 1:00 am.

red dot - to be explained shortly

Zooming in T

“Powers of Ten”, the classic space visualization film by
Charles and Ray Eames, comes to mind. “Powers of Ten” is
an animated journey from the smallest known entities to the largest,
scaling the view by a factor of ten every ten seconds.

Here, rather than zooming in space, we zoom in time. The next stop
in the zoom: 1,000 minutes, or sixteen and two thirds hours. These 1,000
minutes show cab spots from midnight to the beginning of a Thursday afternoon
rush hour.

Cabs are all over town. Airport and commuter traffic has begun to
draw heavy lines along Highways 101 and 280, with mostly the Eastern
side of San Francisco spilling into and out of them.

The red dot has moved a little, but not much.

Zooming by another factor of ten, we arrive at a span of 10,000 minutes,
or nearly a full week. Almost every bit of pavement in town is represented
now.

Finally, here is a Milky Way image of cabs in San Francisco,
a portion of 5,744,623 cab-spots recorded over the course of 31 days
(44,640 minutes) from March 21st to April 21st, 2007.

Zooming out in space as well as time, we get a 31 day view covering most
of the Bay Area. Of course, San Francisco is hottest in this image since
the CabSpotting data comes from the San Francisco fleet of cabs. This zoomed
out view gives a sense of how much traffic the area airports draw from San
Francisco.

Dot Plots

The images here were produced by simply rendering cab-spots to individual
pixels. Each cab-spot is highly translucent so that large accumulations
of spots at a given pixel combine to produce bright pixels and slight
accumulations give faint pixels. This treatment was inspired by Spot
Draves’s log-density technique for rendering his Electric Sheep fractal
flames, gorgeous animations of iterated functional systems (IFSs). The
CabSpotting data is somewhat analogous to IFSs. IFSs depict a sort of
probability density, or the likelihood that a certain calculation will
produce a result at each point in space over many many iterations. The
CabSpotting dot-plots effectively show the likelihood that you could
throw a dart at a grid of points in San Francisco and hit a cab.

Cranking up the cab-spot alpha to make the spots opaque produces "over
exposed" images like the following two, revealing curious anomalies.

In these 31-day views numerous cab-spots surprisingly appear over
the water. A wide swath of mysterious water taxis crosses the bay from
San Francisco to Emeryville and Oakland. Busy lanes are visible within
this swath, as well as to the South. They seem to emanate from dense nodes
on the San Francisco side - from the Yellow Cab Cooperative where Cesar
Chavez crosses 280, and from SFO.

Changes in Latitude

There is a subtle mistake in the black on white spilt-ink first
image above. It is stretched horizontally. The problem
is more pronounced in the following dot-plot, with SOMA streets appearing
skewed, not crossing at right angles.

These images do not account for the fact that unit changes of latitude
and longitude don’t represent the same physical distances when far
from the equator. San Francisco is at almost 38° North. So, changes
in longitude represent shorter physical distances than the same changes
in latitude do. Scaling latitudes of plotted points by about cos 38°,
or 0.788, accommodates for this, making streets cross at right angles once
more.

Fuzz-spots

The cab-spots get rather scattered downtown. There
are not hundreds of cabs parked on rooftops. This fuzziness probably
comes from positions perturbed by reflections in the street canyons among
downtown skyscrapers. From the perspective of a GPS receiver, maybe it
is hard to tell if there is a direct line of sight to a satellite or
the satellite ping is bouncing off a building.

It’s not clear what is going on with the slight swelling
at street intersections in lower-rise areas of town.

Red
Dot

Finally, the red dot.

These cab-spot images typically portray hundreds
of cabs spread out over the Bay Area, with an obvious concentration
in San Francisco. Averaging the positions of all the cabs represented
in a view gives a sort of center of gravity, a cog-spot, of the cab
fleet for that view's span of time. The red dot is the cab fleet's cog-spot.

Coincidentally, the 31-day center-of-gravity is only a few blocks
from Stamen's office.

When we calculate the center of gravity hourly over the course of 31
days (744 hours) we get the caviar view of cog-spots below.
The fleet's center floats mostly North-South, rising to just above Civic
Center and descending South nearly to Cesar Chavez.

There are two outliers in this image. The bright red spot towards the middle
of the image is near Sutro Tower. The more faint spot in the lower right
is the Yellow Cab lot near 280. There must have been an hour-long
period where the system only took positions of cabs at the lot. The density
of the red spot just above Sutro Tower suggests there were several hours
when the system reported positions there.

The next image shows the hourly cog-spots from midnight to 4:00 PM on
March 21st. The spots are colored from green at midnight to
red at 4:00 PM. The fleet's center of gravity begins near Civic Center
at midnight, drops South in the morning, and drifts East toward the freeways
in the afternoon.

This last collection of red dots shows the accumulation of hour-of-day
cog-spots over the course of a week. This essentially stretches the span
in the image above to fill a day, then takes seven successive day long
samples like this and averages them. The week long pattern is similar to
the one day pattern.